Simultaneous minimization of total completion time and total deviation of job completion times

Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


This paper addresses a single-machine scheduling problem with the objective of minimizing a linear combination of total job completion times and total deviation of job completion times from a common due-date. The due-date is assumed to be non-restrictive, i.e., sufficiently large to have no impact on the optimal sequence. When the weights are job-independent, the problem is shown to have a polynomial time solution, and the optimal schedule is fully characterized as a function of the different parameters. When job-dependent weights are assumed, the problem is known to be NP-hard. We introduce a pseudo-polynomial dynamic programming algorithm, indicating that this case is NP-hard in the ordinary sense. The algorithm is shown experimentally to perform extremely well when tested on high-multiplicity instances with up to 1000 jobs.

Original languageAmerican English
Pages (from-to)296-306
Number of pages11
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - 1 Sep 2004

Bibliographical note

Funding Information:
This paper was supported in part by the Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.


  • Deterministic
  • Dynamic programming
  • Multiple criteria
  • Pseudo-polynomial algorithm
  • Scheduling
  • Single machine


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